I agree. In my game, most civilzations had comparable tech. Therefore, they would have had nuke capability eventually. However, looking back, it seems stupid to make the Manhattan Project. I should have just let another civ waste their money building because I would have gain the nuke capabilty either way.
Also, according to the manual and the civ encyclopedia, you don't need to build the Manhattan Project (which is listed as a great wonder) to make nukes. This is different from the game play. I believe this is a bug.
Lastly, I must comment that this is not an easy game. I played Civ I long time ago, and the chieftain level in civ III is more difficult than the prince level in the old civ I. I hope they make a new patch to make this game easier to play at the chieftain level.